Context Driven Topologies are mathematical groups of ideas and information transmitted over computers and networks. Their form and process are expressed using drawings and specifications. Their purpose is to organize and drive network topologies to answer questions and derive meaning from data collections of any size, particularly in open source environments. The purpose of answering questions and deriving meaning is to foster Collective Intelligence. Refer to Wikipedia Unassessed Systems for related work.

The default form envisioned for storage mode is a spiral. Groups of ideas and information can be rearranged infinite ways while working with or distributing to and from precise locations. Locations can be physical, conceptual, or a combination of both. Assuming constructing exchanges and working this way is possible, what shapes and topologies would be most effective? What are their properties? What do they have in common? What would a computer and network language about these pathways, densities, colors, transparencies, forms, linkages and exchanges look like?

Its too complicated to wonder about ALL possible forms, the question can be simplified by just concentrating on spirals for an example. Therefore, a previous post Spiral Model is expanded to incorporate slides prepared by A&A Director Vera W. de Spinadel for a Postgraduate class on Form and Mathematics which focuses on logic and technique. Dr. de Spindel remarks “Of course this has a lot to do with the subject of Context Driven Topologies“. Lets see what this means to computers and networks, starting with :

According to Wikipedia on November 22, 2006: The spiral model is a software development process combining elements of both design and prototyping-in-stages, in an effort to combine advantages of top-down and bottom-up concepts. What a perfect shape spirals are to portray complex evolving relationships. Just imagine the possibilities using spirals as a base structure.

English captions to be completed at a later date – this slide says “Carrying out some modifications in the process of construction of this spiral, we are going to build other linked with the Numbers of the FNMPP. In the following figure details of the construction are shown.”

Of course spirals are seen in nature and architecture. Rough translation “Finally, in the country of the Architectural Design, fits to mention the interesting antecedent of the Spiral building, built by the Arq. Fumihiko Maki in Tokyo, Japan in 1985. Maki gue prizewinner with the Prize Pritzker in 1993 and in its Spiral building has utilized the geometry of the curve, that conjugates marvelously the concepts of fragment and unattainable center. The geometric figure is an evocation of the ones that are found in Kyoto, in the famous Temple of Ginkakuji (Silver Building) 1338-1573 and in the Temple of Kinkakuji (Building of Gold) 1398, reconstructed in 1955. Though these denominations of Gold and Silver have religious and historic meaning, they would be able to serve of example to design making use of so much, metallic spirals flat curves like helicoides metallic.”

The question Vera is looking for is geometrical interpretations of the members of the family of metallic means – which she discovered in 1997. She found a relationship of the golden mean with the pentagon and another of the silver mean with the octagon. And that was all, there were no more relationships with polygons. So, she began trying to construct metallic spirals, generalizing the well known golden spiral – and was successful! She introduced a family of metallic spirals and continues intensively working with the silver spiral. There will be more to see when she presents at the International Conference on Geometry and Graphics ICGG-2008 in Dresden Germany.

Other computer and network systems that may be interesting to study in terms of forms, dynamic properties, geometry and graphics to streamline information that have been highlighted in recent discussions include:

the Information Economy Meta Language IEML see the paper “Collective Intelligence Protocol Semantic Metadata Exchange Standard (CIP-SMES)” by Michel Bietzunski and Steven Newcomb 18 July 2007. A commentary on this paper and Chapter 3 of Topic Maps by the same authors, edited by Jack Park is here IEMLcomments